Domain wall dynamics driven by spin transfer torque and the spin-orbit field

We have studied current-driven dynamics of domain walls when an in-plane magnetic field is present in perpendicularly magnetized nanowires using an analytical model and micromagnetic simulations. We model an experimentally studied system, ultrathin magnetic nanowires with perpendicular anisotropy, where an effective in-plane magnetic field is developed when current is passed along the nanowire due to the Rashba-like spin-orbit coupling. Using a one-dimensional model of a domain wall together with micromagnetic simulations, we show that the existence of such in-plane magnetic fields can either lower or raise the threshold current needed to cause domain wall motion. In the presence of the in-plane field, the threshold current differs for positive and negative currents for a given wall chirality, and the wall motion becomes sensitive to out-of-plane magnetic fields. We show that large non-adiabatic spin torque can counteract the effect of the in-plane field.     

Influence of exchange coupling on current-driven domain wall motion in a nanowire

In this study, the effect of exchange stiffness constant on current-driven domain wall motion in nanowires with in-plane magnetic anisotropy (IMA) and perpendicular magnetic anisotropy (PMA) has been investigated using micromagnetic simulation. The critical current density in a nanowire with IMA decreases as the exchange stiffness constant decreases because the domain wall width at the upper edge of the nanowire narrows according to the decrease of the exchange stiffness constant. On the other hand, the critical current density in a nanowire with PMA slightly decreases contrary to that of IMA although the domain wall width reasonably decreases as the exchange stiffness constant decreases. The slight reduction rate of the critical current density is due to the increase of the effective hard-axis anisotropy of PMA nanowire.     

Current-driven magnetization switching and domain wall motion in nanostructures—Survey of recent experiments

An overview of recent experimental studies and new routes in the field of current-driven magnetization dynamics in nanostructured materials is given. The review introduces the basic concepts (Landau–Lifshitz phenomenology, critical current, spin currents in relation to spin accumulation, adiabatic/non-adiabatic spin-torque) and describes the main results of recent experiments on current-driven magnetization reversal within vertical pillar-like nanostructures and current-driven domain wall motion within laterally confined specimens. While for the pillar systems a discussion is provided of how the introduction of layers with perpendicular magnetic anisotropy, tunnel barriers and exchange bias and(or) oxide layers can be used to reduce the critical current densities for current-induced switching, the role of perpendicular anisotropy, use of spin valve structures, diluted magnetic semiconductors and epitaxial materials to increase the domain wall velocities are reviewed in the case of current-driven domain wall movement within lateral systems.     

Domain wall motion in ferromagnetic systems with perpendicular magnetization

Although we lack clear experimental evidence, apparently out-of-plane magnetized systems are better suited for spintronic applications than the in-plane magnetized ones, mainly due to the smaller current densities required for achieving domain wall motion. [Co/Pt] multilayers belong to the first category of materials, the out-of-plane magnetization orientation arising from the strong perpendicular magnetocrystalline anisotropy. If the magnetization arranges itself out-of-plane narrow Bloch walls occur. In the present paper, both field and current-driven domain wall motion have been investigated for this system, using micromagnetic simulations. Three types of geometries have been taken into account: bulk, thin film and wire, and for all of them a full comparison is done between the effect of the applied field and injected current. The reduction of the system's dimension induces the decrease of the critical field and the critical current, but it does not influence the domain wall displacement mechanism.     

Current-induced domain wall motion with adiabatic and nonadiabatic spin torques in magnetic nanowires

We investigate current-driven domain wall (DW) propagation in magnetic nanowires in the framework of the modified Landau-Lifshitz-Gilbert equation with both adiabatic and nonadiabatic spin torque (AST and NAST) terms. By employing a simple analytical model, we can demonstrate the essential physics that any small current density can drive the DW motion along a uniaxial anisotropy nanowire even in absence of NAST, while a critical current density threshold is required due to intrinsic anisotropy pinning in a biaxial nanowire without NAST. The DW motion along the uniaxial wire corresponds to the asymptotical DW oscillation solution under high field/current in the biaxial wire case. The current-driven DW velocity weakly depends on the NAST parameter β in a uniaxial wire and it is similar to the β = α case (α: damping) in the biaxial wire. Apart from that, we discuss the rigid DW motion from both the energy and angular momentum viewpoints and point out some physical relations in between. We also propose an experimental scheme to measure the spin current polarization by combining both field- and current-driven DW motion in a usual flat (biaxial) nanowire.     

Concept of the field-driven domain wall motion memory

In this paper, the concept of field-driven domain wall motion memory is presented. It is confirmed that a domain is shifted with a carefully designed non-uniform field by micromagnetic simulations. The shift of a domain—a bit—can be established by the motion of two domain walls to the same direction and the same distance. In order to get a better understanding of the domain wall motion under the non-uniform transverse magnetic field, we investigate the motion of the transverse Néel-type domain wall by micromagnetic simulations and the collective coordinate approach. The validity of the equation of motion for the domain wall is confirmed by the micromagnetic simulations as functions of the gradient of the non-uniform field, the saturation magnetization, and the Gilbert damping parameter α.     

Faster 360° domain wall motion in nanostrip induced by spin-polarized current with out-of-plane magnetic field

By micromagnetic simulation, we show that faster propagation of 360° domain wall in magnetic nanostrips under spin-polarized currents in conjunction with out-of-plane magnetic fields can be obtained. Without magnetic field, the annihilation process of 360° domain wall is irreversible when spin-polarized current velocity above about 220 m/s. The annihilation of 360° domain wall can be suppressed by an out-of -plane magnetic field and domain wall speed can exceed 1500 m/s at large current density. This is different from the case exhibited in 180° domain wall. The underlying mechanism is investigated by changing the state of 360° domain wall and the direction of out-of-plane field.     

Micromagnetic study of domain wall depinning driven by nanosecond current pulse in notched Permalloy nanowires

The complete understanding of domain wall (DW) dynamics is important in the design of future spintronic devices. The characteristics of faster time-scale and lower current amplitude to move DW along nanowire are crucial in fabrication upgrade. In this study, we have investigated depinning behavior of magnetic domain wall triggered by nanosecond current pulse in notched Permalloy nanowires by means of micromagnetic simulation. We introduced double-triangular notch as the constrictions in the nanowire. The non-adiabaticity of the spin-transfer-torque is considered in simulation by varying the non-adiabatic constant (β) value. We observed that the depinning current density (J_d) was not significantly affected by β for notch size (s) < 50 nm. Interestingly, we found that the depinning time (t_d) for β ≥ 0.04 was slightly constant for all the cases with s > 70 nm, where the DW structure was kept to be a transverse structure during the depinning process. The broadly applicable depinning behavior is considered to contribute to the development of high-speed memory storage devices based on magnetic domain wall.     

Current induced domain wall motion in nanostripes with perpendicular magnetic anisotropy

We report micromagnetic modeling results of current induced domain wall (DW) motion in magnetic devices with perpendicular magnetic anisotropy by solving the Landau-Lifschitz-Gilbert equation including adiabatic and non-adiabatic terms. A nanostripe model system with dimensions of 500 nm (L)×25 nm (W)×5 nm (H) was selected for calculating the DW motion and its width, as a function of various parameters such as non-adiabatic contribution, anisotropy constant (K_u), saturation magnetization (M_s), and temperature (T). The DW velocity was found to increase when the values of K_u and T were increased and the M_s value decreased. In addition, a reduction of the domain wall width could be achieved by increasing K_u and lowering M_s values regardless of the non-adiabatic constant value.     

Controlled domain wall motion by current into patterned-U Ni80Fe20 wires

The current-induced domain wall motion was observed experimentally in the case of the domain wall trapped at the semicircular arc within the U shape Ni₈₀Fe₂₀ wire. The measurement of the current-induced domain wall motion was achieved by adding a biased field before switching field and a critical current density was measured. We found two magnetic domain structures in the U pattern. At zero fields, the vortex domain wall nucleated at the semicircular arc of the U pattern. Continuous magnetic state without wall was investigated in near-switching field.     

Nonmonotonic effects of perpendicular magnetic anisotropy on current-driven vortex wall motions in magnetic nanostripes

In a magnetic nanostripe, the effects of perpendicular magnetic anisotropy(PMA) on the current-driven horizontal motion of vortex wall along the stripe and the vertical motion of the vortex core are studied by micromagnetic simulations.The results show that the horizontal and vertical motion can generally be monotonously enhanced by PMA. However, when the current is small, a nonmonotonic phenomenon for the horizontal motion is found. Namely, the velocity of the horizontal motion firstly decreases and then increases with the increase of the PMA. We find that the reason for this is that the PMA can firstly increase and then decrease the confining force induced by the confining potential energy. In addition, the PMA always enhances the driving force induced by the current.     

消磁场对纳米铁磁线磁畴壁动力学行为的影响

为了实现基于磁畴壁运动的自旋电子学装置, 掌握磁畴壁动力学行为是重要争论之一.研究了在外磁场驱动下L-型纳米铁磁线磁畴壁的动力学行为. 通过微磁学模拟,在各种外磁场的驱动下考察了纳米铁磁线磁畴壁的动力学特性; 在较强外磁场的驱动下, 在不同厚度纳米线上考察了纳米线表面消磁场对磁畴壁动力学行为的影响. 为了进一步证实消磁场对磁畴壁动力学的影响, 在垂直于纳米线表面的外磁场辅助下分析了磁畴壁的动力学行为变化. 结果表明, 随着纳米线厚度和外驱动磁场强度的增加, 增强了纳米线表面的消磁场的形成, 使得磁畴壁内部自旋结构发生周期性变化, 导致磁畴壁在纳米线上传播时出现Walker崩溃现象. 在垂直于纳米线表面的外磁场辅助下, 发现辅助磁场可以调节消磁场的强度和方向. 这意味着利用辅助磁场可以有效地控制纳米铁磁线磁畴壁的动力学行为.     

Nanometer scale observation of high efficiency thermally assisted current-driven domain wall depinning

Nanometer scale observation of the depinning of a narrow domain wall (DW) under a spin current is reported. We studied approximately 12 nm wide 1D Bloch DWs created in thin films exhibiting perpendicular magnetic anisotropy. Magnetotransport measurements reveal thermally assisted current-driven DW motion between pinning sites separated by as little as 20 nm. The efficiency of current-driven DW motion assisted by thermal fluctuations is measured to be orders of magnitude higher than has been found for in-plane magnetized films, allowing us to control DW motion on a nanometer scale at low current densities.     

The influence of the geometry of micro-patterned thin films on the effective permeability and resonance frequency by domains development

For the application in high-frequency micromagnetic devices, the permeability and resonance frequency of ferromagnetic components is of high interest. It is dominantly influenced by different factors, the external field and direction and the domain distribution, shape and orientation. By the use of micromagnetic simulation, the domain pattern in films was determined and the effective permeability was calculated. The results of the calculations were compared with the domain shape of patterned microstructures of thin FeCoTaN-films, which were deposited onto oxidised silicon substrates by reactive r.f.-magnetron sputtering by employing 6-in Fe₃₇Co₄₆Ta₁₇ targets. To achieve a high-frequency suitability, the films have to be annealed in a static magnetic field of 50 mT between 400 and 500 °C, which are typical temperatures used in CMOS processes, to induce an in-plane uniaxial anisotropy needed for the high-frequency performance. Magnetic softness was obtained by producing amorphous or nanocrystalline films, and additionally, by aspiring low magnetocrystalline anisotropies for, e.g., certain Fe/Co fractions. The unpatterned films with a lateral dimension of 5×5 mm² were measured in a strip line permeameter in a frequency range up to 5 GHz and exhibited ferromagnetic resonance frequencies between 2 and 2.5 GHz within a low-loss permeability spectrum (low width of imaginary part of permeability). For possible integrations in passive microelectronic components the films were patterned to a few tenths of micrometers by near ultra-violet lithography and plasma beam etching, and then consequently annealed to obtain the static and dynamic magnetic properties. To influence the amount of closure domains, designs were conceived to influence the domain formation by creating additional internal boundaries. As a result, the ferromagnetic resonance frequency and the effective permeability are strongly driven by internal and external boundaries.     

Current induced domain wall motion in GaMnAs close to the Curie temperature

Domain wall dynamics produced by spin transfer torques is investigated in (Ga, Mn)As ferromagnetic semiconducting tracks with perpendicular anisotropy, close to the Curie temperature. The domain wall velocities are found to follow a linear flow regime which only slightly varies with temperature. Using the D?ring inequality, boundaries of the spin polarization of the current are deduced. A comparison with the predictions of the mean field k·p theory leads to an estimation of the carrier density whose value is compatible with results published in the literature. The spin polarization of the current and the magnetization of the magnetic atoms present similar temperature variations. This leads to a weak temperature dependence of the spin drift velocity and thus of the domain wall velocity. A combined study of field- and current-driven motion and deformation of magnetic domains reveals a motion of domain walls in the steady state regime without transition to the precessional regime. The ratio between the non-adiabatic torque β and the Gilbert damping factor α is shown to remain close to unity.     

Numerical simulation of wall dynamics in (111)-oriented garnet films in the presence of an in-plane magnetic field

The domain wall motion in the presence of an in-plane magnetic field H_y perpendicular to the wall is simulated using a fall implicit numerical scheme. Calculations are performed for the drive fields 0 Oe<H_z<15 Oe and in-plane fields -210 Oe?H_y?210 Oe. The relation between the average wall velocity $\text{v}$ and the drive field H_z is discussed considering the wall structure. It was found that an in-plane field increases the peak velocity of the wall and extends the range of the drive fields, where the linear mobility relation is valid. A dynamical Bloch line stacking was found for sufficiently large drives. The influence of an in-plane field on the angular span of horizontal Bloch lines is discussed also. In particular the occurrence of 2π-horizontal Bloch lines is described. Numerical results obtained with a full implicit method are compared with the experimental observations of bubble motion and good agreement is found for |H_y|≤100 Oe.     

无序二维约瑟夫森结阵列中磁场引起的涡旋玻璃态相变

采用电阻阻错结的无序二维约瑟夫森结阵列模型,数值研究超导薄膜中垂直磁场引起的涡旋运动.通过分析磁场激发产生的涡旋度Ne及低频电压噪声S₀的变化特性,得到如下结论：在无序超导体中固定温度不变,随着磁场的减弱涡旋液态经过准有序的布拉格相,涡旋玻璃相重新进入到低磁场下的钉扎稀磁液相. 由于在涡旋玻璃相中,电流驱动下的噪声值表现出一个峰,表明系统处于无序与有序相互竞争的亚稳态,并且临界电流应有峰值效应. 计算得到噪声值的变化与Okuma等得到的无序超导Mo_xSi_1-x膜实验现象一致,并能解释磁场降低引起的重新进入钉扎的稀磁液相行为. 关键词： 约瑟夫森结阵列 磁通玻璃 重新进入 峰值效应     

The stochastic nature of the domain wall motion along high perpendicular anisotropy strips with surface roughness

The domain wall dynamics along thin ferromagnetic strips with high perpendicular magnetocrystalline anisotropy driven by either magnetic fields or spin-polarized currents is theoretically analyzed by means of full micromagnetic simulations and a one-dimensional model, including both surface roughness and thermal effects. At finite temperature, the results show a field dependence of the domain wall velocity in good qualitative agreement with available experimental measurements, indicating a low field, low velocity creep regime, and a high field, linear regime separated by a smeared depinning region. Similar behaviors were also observed under applied currents. In the low current creep regime the velocity-current characteristic does not depend significantly on the non-adiabaticity. At high currents, where the domain wall velocity becomes insensitive to surface pinning, the domain wall shows a precessional behavior even when the non-adiabatic parameter is equal to the Gilbert damping. These analyses confirm the relevance of both thermal fluctuations and surface roughness for the domain wall dynamics, and that complete micromagnetic modeling and one-dimensional studies taking into account these effects are required to interpret the experimental measurements in order to get a better understanding of the origin, the role and the magnitude of the non-adiabaticity.     

Micromagnetic simulations of the magnetization dynamics in nanostructures with special applications to spin injection

We present several micromagnetic simulation examples of magnetization dynamics driven by the spin injection. First, we address the validity of the macrospin approximation often used to interpret experimental data. Next, we discuss the interpretation of experimental results obtained on columnar multilayer structures and show that a sophisticated micromagnetic model which takes into account a polycrystalline structure of a nanoelement can explain qualitatively the most important features of the magnetization oscillation spectra observed experimentally. A quantitative agreement with experimental results, however, could not be achieved in the region of reasonable parameter values. The third part of our contribution deals with simulations of the point-contact experiments. Here, we find an important qualitative disagreement between the experiment and simulations. The latter predict the existence of two current regions of a steady-state precession of the point-contact area (before and after spin-polarized current-driven magnetization switching), whereas experimentally only one such region is observed. In conclusion, we discuss some explanations of the above-mentioned discrepancies.     

Domain wall creation in nanostructures driven by a spin-polarized current

We report on current-driven magnetization reversal in nanopillars with elements having perpendicular magnetic anisotropy. Whereas only the two uniform magnetization states are available under the action of a magnetic field, we observed current-induced Bloch domain walls in pillars as small as 50 x 100 nm(2). This domain wall state can be further controlled by current to restore the uniform states. The ability to nucleate and manipulate domain walls by a current gives insight into the reversal mechanisms of small nanoelements and provides new prospects for ultrahigh density spintronic devices.